Using the Correct Rule(s) Examples

Example 1

Find the derivative of

This function contains both a product and a quotient. Since the quotient is "outside" the product (that is, we would find the quotient after finding the product x2sin x), we start with the quotient rule.

Now we need to use the product rule, in order to find one of the derivatives we need to finish applying the quotient rule!

(x2sin x)' = 2xsin x + x2cos x.

Then we can go back and finish with the quotient rule:

Example 2

Find the derivative of

This function contains both a product and a quotient, and in this case the product is "outside" the quotient. We start with the product rule:

In order to complete the use of the product rule, we need to find the derivative of the quotient:

Now we can put this back into the product rule and finish the problem.